Wald's airplane damage story is a favorite example of one of my statistics professors. Humbling example of how statistics can easily be misinterpreted, at least for me. I can see myself making this kind of mistake (that the officers made).
I highly recommend Ellenberg's "How Not To Be Wrong". Ellenberg is a first-class mathematician and general expositor, and his book illustrates the power (and the limitation, in an endearing way) of mathematics as a tool of thought.